Barton, Nick HIST Austria ; Etheridge, Alison; Véber, Amandine
We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large scale extinction-recolonisation events. The lineages ancestral to a sample from a population evolving according to this model can be described in terms of a spatial version of the Lambda-coalescent. Using a technique of Evans (1997), we prove existence and uniqueness in law for the model. We then investigate the asymptotic behaviour of the genealogy of a finite number of individuals sampled uniformly at random (or more generally `far enough apart') from a two-dimensional torus of sidelength L as L tends to infinity. Under appropriate conditions (and on a suitable timescale) we can obtain as limiting genealogical processes a Kingman coalescent, a more general Lambda-coalescent or a system of coalescing Brownian motions (with a non-local coalescence mechanism).
Electronic Journal of Probability
162 - 216
Barton NH, Etheridge A, Véber A. A new model for evolution in a spatial continuum. Electronic Journal of Probability. 2010;15(7):162-216. doi:10.1214/EJP.v15-741
Barton, N. H., Etheridge, A., & Véber, A. (2010). A new model for evolution in a spatial continuum. Electronic Journal of Probability, 15(7), 162–216. https://doi.org/10.1214/EJP.v15-741
Barton, Nicholas H, Alison Etheridge, and Amandine Véber. “A New Model for Evolution in a Spatial Continuum.” Electronic Journal of Probability 15, no. 7 (2010): 162–216. https://doi.org/10.1214/EJP.v15-741.
N. H. Barton, A. Etheridge, and A. Véber, “A new model for evolution in a spatial continuum,” Electronic Journal of Probability, vol. 15, no. 7, pp. 162–216, 2010.
Barton NH, Etheridge A, Véber A. 2010. A new model for evolution in a spatial continuum. Electronic Journal of Probability. 15(7), 162–216.
Barton, Nicholas H., et al. “A New Model for Evolution in a Spatial Continuum.” Electronic Journal of Probability, vol. 15, no. 7, Institute of Mathematical Statistics, 2010, pp. 162–216, doi:10.1214/EJP.v15-741.
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